Surface area of a cylinder


When working out the surface area of a cylinder, remember to consider both circular ends and the curved surface.



What is the surface area of a cylinder?

The total of both the circular end areas and the curved surface area.


Surface area of cylinder formula

Cylinder surface area  =  both circular end areas  +  curved surface area



The area of each end of the cylinder is πr² (where π= pi and r = radius of circle) (see also area of a circle). So the area of both ends of the cylinder is 2πr².


The curved surface area is the circumference of the cylinder (2πr - see also circumference of a circle) multiplied by its height (h), i.e. 2πr x h = 2πrh.


Hence, the surface area of a cylinder formula becomes



where SAcylinder = surface area of cylinder.


Let's take a look at an example calculation

Consider a cylinder with radius (r) 1cm and height (h) 5cm (where cm = centimeters) - calculate its surface area.


SAcylinder

=   2πr²  +   2πrh

=   (2 x π x 1²)  +  (2 x π x 1 x 5)

=  37.7cm² (square centimeters) to 1 d.p. (one decimal place)


Remember to use the left and right bracket buttons on your calculator.




The calculator key strokes are left bracket, 2, multiply sign (x), pi sign (π), multiply sign (x), 1, squared sign (x²), right bracket, add sign (+), left bracket, 2, multiply sign, pi sign (π), multiply sign (x), 1, multiply sign (x), 5, right bracket, equals sign (=). Your calculator should display 37.69911184 which is 37.7 to 1 d.p. You may need to access x² and π via a shift or 2nd function button.


Another example


Work out SAcylinder given r = 2cm and h = 10cm.


SAcylinder

=   2πr²  +   2πrh

=   (2 x π x 2²)  +  (2 x π x 2 x 5)

=  88.0cm² (square centimeters) to 1 d.p. (one decimal place)


See if you get this answer on your calculator - 88.0cm² is rounded up from the 87.9645943 which should be displayed on your calculator screen at the end of your calculation.


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Volume of a cylinder

Volume of a cone

Surface area of a cone


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